Find the ratio of kinetic energies of two bodies of masses 1kg and 4 kg equal linear momenta.

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Solution

Let $m_{1} = 1 k g$ and $m_{2} = 4 k g$

Given that
$m_{1} v_{1} = m_{2} v_{2}$

$\frac{v_{1}}{v_{2}} = \frac{m_{2}}{m_{1}}$

$∴$ Ratio between their kinetic energies , $= \frac{K_{1}}{K_{2}} = \frac{\frac{1}{2} m_{1} v_{1}^{2}}{\frac{1}{2} m_{2} v_{2}^{2}}$

$⟹ \frac{K_{1}}{K_{2}} = \frac{m_{1}}{m_{2}} \times \frac{m_{2}^{2}}{m_{1}^{2}} = \frac{m_{2}}{m_{1}} = 4$

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